"Just because we're of the same party doesn't mean we're not going to look at this closely," Sen. Arlen Specter, R-Pa,, said on "This Week" on ABC.
Specter plans to hold committee hearings on the matter next month, with witnesses to include Attorney General Alberto Gonzales, The New York Times reported.
Specter has said he does not agree with the White House view that Congress effectively authorized the National Security Agency surveillance in a resolution passed shortly after the Sept. 11, 2001, terrorist attacks.
He said if Bush were found to have acted illegally, he would most likely face "a political price" rather than impeachment -- in part because of what he called broad support for the administration's efforts against terrorism.
"I don't see any talk about impeachment here," Specter said. "I don't think anybody doubts that the president is making a good faith effort here, that he sees a real problem, as we all do, and he's acting in a way that he feels he must."